Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,2,Mod(1,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(8.69570878012\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.618034 | −0.437016 | −0.218508 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218508 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | 2.61803 | 1.17082 | 0.585410 | − | 0.810737i | \(-0.300933\pi\) | ||||
0.585410 | + | 0.810737i | \(0.300933\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.00000 | −1.13389 | −0.566947 | − | 0.823754i | \(-0.691875\pi\) | ||||
−0.566947 | + | 0.823754i | \(0.691875\pi\) | |||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.61803 | −0.511667 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.76393 | −0.489227 | −0.244613 | − | 0.969621i | \(-0.578661\pi\) | ||||
−0.244613 | + | 0.969621i | \(0.578661\pi\) | |||||||
\(14\) | 1.85410 | 0.495530 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | 1.61803 | 0.392431 | 0.196215 | − | 0.980561i | \(-0.437135\pi\) | ||||
0.196215 | + | 0.980561i | \(0.437135\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.85410 | −1.34302 | −0.671512 | − | 0.740994i | \(-0.734355\pi\) | ||||
−0.671512 | + | 0.740994i | \(0.734355\pi\) | |||||||
\(20\) | −4.23607 | −0.947214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.47214 | −0.723990 | −0.361995 | − | 0.932180i | \(-0.617904\pi\) | ||||
−0.361995 | + | 0.932180i | \(0.617904\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.85410 | 0.370820 | ||||||||
\(26\) | 1.09017 | 0.213800 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.85410 | 0.917339 | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.85410 | 0.512612 | 0.256306 | − | 0.966596i | \(-0.417495\pi\) | ||||
0.256306 | + | 0.966596i | \(0.417495\pi\) | |||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | −7.85410 | −1.32759 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.236068 | 0.0388093 | 0.0194047 | − | 0.999812i | \(-0.493823\pi\) | ||||
0.0194047 | + | 0.999812i | \(0.493823\pi\) | |||||||
\(38\) | 3.61803 | 0.586923 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.85410 | 0.925615 | ||||||||
\(41\) | −11.9443 | −1.86538 | −0.932691 | − | 0.360677i | \(-0.882546\pi\) | ||||
−0.932691 | + | 0.360677i | \(0.882546\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.23607 | −0.950991 | −0.475496 | − | 0.879718i | \(-0.657731\pi\) | ||||
−0.475496 | + | 0.879718i | \(0.657731\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.14590 | 0.316395 | ||||||||
\(47\) | −1.61803 | −0.236015 | −0.118007 | − | 0.993013i | \(-0.537651\pi\) | ||||
−0.118007 | + | 0.993013i | \(0.537651\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | −1.14590 | −0.162054 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.85410 | 0.395793 | ||||||||
\(53\) | 9.61803 | 1.32114 | 0.660569 | − | 0.750765i | \(-0.270315\pi\) | ||||
0.660569 | + | 0.750765i | \(0.270315\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.70820 | −0.896421 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.76393 | −0.362922 | ||||||||
\(59\) | −10.3262 | −1.34436 | −0.672181 | − | 0.740387i | \(-0.734642\pi\) | ||||
−0.672181 | + | 0.740387i | \(0.734642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.85410 | −1.00561 | −0.502807 | − | 0.864398i | \(-0.667699\pi\) | ||||
−0.502807 | + | 0.864398i | \(0.667699\pi\) | |||||||
\(62\) | −1.76393 | −0.224020 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | −4.61803 | −0.572797 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.56231 | −1.16822 | −0.584111 | − | 0.811674i | \(-0.698557\pi\) | ||||
−0.584111 | + | 0.811674i | \(0.698557\pi\) | |||||||
\(68\) | −2.61803 | −0.317483 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.85410 | 0.580176 | ||||||||
\(71\) | 5.56231 | 0.660124 | 0.330062 | − | 0.943959i | \(-0.392930\pi\) | ||||
0.330062 | + | 0.943959i | \(0.392930\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.23607 | 0.378753 | 0.189377 | − | 0.981905i | \(-0.439353\pi\) | ||||
0.189377 | + | 0.981905i | \(0.439353\pi\) | |||||||
\(74\) | −0.145898 | −0.0169603 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.47214 | 1.08653 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.47214 | −1.06570 | −0.532849 | − | 0.846210i | \(-0.678879\pi\) | ||||
−0.532849 | + | 0.846210i | \(0.678879\pi\) | |||||||
\(80\) | 4.85410 | 0.542705 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.38197 | 0.815202 | ||||||||
\(83\) | 0.708204 | 0.0777355 | 0.0388677 | − | 0.999244i | \(-0.487625\pi\) | ||||
0.0388677 | + | 0.999244i | \(0.487625\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.23607 | 0.459466 | ||||||||
\(86\) | 3.85410 | 0.415599 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.527864 | −0.0559535 | −0.0279767 | − | 0.999609i | \(-0.508906\pi\) | ||||
−0.0279767 | + | 0.999609i | \(0.508906\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.29180 | 0.554731 | ||||||||
\(92\) | 5.61803 | 0.585721 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.00000 | 0.103142 | ||||||||
\(95\) | −15.3262 | −1.57244 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.0344 | −1.42498 | −0.712491 | − | 0.701681i | \(-0.752433\pi\) | ||||
−0.712491 | + | 0.701681i | \(0.752433\pi\) | |||||||
\(98\) | −1.23607 | −0.124862 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | −0.300000 | ||||||||
\(101\) | −3.00000 | −0.298511 | −0.149256 | − | 0.988799i | \(-0.547688\pi\) | ||||
−0.149256 | + | 0.988799i | \(0.547688\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.00000 | −0.591198 | −0.295599 | − | 0.955312i | \(-0.595519\pi\) | ||||
−0.295599 | + | 0.955312i | \(0.595519\pi\) | |||||||
\(104\) | −3.94427 | −0.386768 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.94427 | −0.577359 | ||||||||
\(107\) | −4.23607 | −0.409516 | −0.204758 | − | 0.978813i | \(-0.565641\pi\) | ||||
−0.204758 | + | 0.978813i | \(0.565641\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.56231 | −0.525589 | ||||||||
\(113\) | −0.708204 | −0.0666222 | −0.0333111 | − | 0.999445i | \(-0.510605\pi\) | ||||
−0.0333111 | + | 0.999445i | \(0.510605\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.09017 | −0.847663 | ||||||||
\(116\) | −7.23607 | −0.671852 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.38197 | 0.587508 | ||||||||
\(119\) | −4.85410 | −0.444975 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 4.85410 | 0.439470 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.61803 | −0.414712 | ||||||||
\(125\) | −8.23607 | −0.736656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.70820 | 0.329050 | 0.164525 | − | 0.986373i | \(-0.447391\pi\) | ||||
0.164525 | + | 0.986373i | \(0.447391\pi\) | |||||||
\(128\) | 11.3820 | 1.00603 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.85410 | 0.250321 | ||||||||
\(131\) | −7.14590 | −0.624340 | −0.312170 | − | 0.950026i | \(-0.601056\pi\) | ||||
−0.312170 | + | 0.950026i | \(0.601056\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.5623 | 1.52285 | ||||||||
\(134\) | 5.90983 | 0.510532 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.61803 | 0.310244 | ||||||||
\(137\) | −7.47214 | −0.638388 | −0.319194 | − | 0.947689i | \(-0.603412\pi\) | ||||
−0.319194 | + | 0.947689i | \(0.603412\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.854102 | 0.0724440 | 0.0362220 | − | 0.999344i | \(-0.488468\pi\) | ||||
0.0362220 | + | 0.999344i | \(0.488468\pi\) | |||||||
\(140\) | 12.7082 | 1.07404 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.43769 | −0.288485 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.7082 | 0.972313 | ||||||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.381966 | −0.0313974 | ||||||||
\(149\) | 15.0000 | 1.22885 | 0.614424 | − | 0.788976i | \(-0.289388\pi\) | ||||
0.614424 | + | 0.788976i | \(0.289388\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.00000 | −0.162758 | −0.0813788 | − | 0.996683i | \(-0.525932\pi\) | ||||
−0.0813788 | + | 0.996683i | \(0.525932\pi\) | |||||||
\(152\) | −13.0902 | −1.06175 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.47214 | 0.600176 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.70820 | −0.295947 | −0.147973 | − | 0.988991i | \(-0.547275\pi\) | ||||
−0.147973 | + | 0.988991i | \(0.547275\pi\) | |||||||
\(158\) | 5.85410 | 0.465727 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −14.7082 | −1.16279 | ||||||||
\(161\) | 10.4164 | 0.820928 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.2705 | 1.43106 | 0.715528 | − | 0.698584i | \(-0.246186\pi\) | ||||
0.715528 | + | 0.698584i | \(0.246186\pi\) | |||||||
\(164\) | 19.3262 | 1.50913 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.437694 | −0.0339717 | ||||||||
\(167\) | 10.0344 | 0.776488 | 0.388244 | − | 0.921557i | \(-0.373082\pi\) | ||||
0.388244 | + | 0.921557i | \(0.373082\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.88854 | −0.760657 | ||||||||
\(170\) | −2.61803 | −0.200794 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.0902 | 0.769368 | ||||||||
\(173\) | 15.3820 | 1.16947 | 0.584735 | − | 0.811225i | \(-0.301199\pi\) | ||||
0.584735 | + | 0.811225i | \(0.301199\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.56231 | −0.420471 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.326238 | 0.0244526 | ||||||||
\(179\) | 2.23607 | 0.167132 | 0.0835658 | − | 0.996502i | \(-0.473369\pi\) | ||||
0.0835658 | + | 0.996502i | \(0.473369\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.4721 | −1.29869 | −0.649347 | − | 0.760492i | \(-0.724958\pi\) | ||||
−0.649347 | + | 0.760492i | \(0.724958\pi\) | |||||||
\(182\) | −3.27051 | −0.242426 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.76393 | −0.572365 | ||||||||
\(185\) | 0.618034 | 0.0454388 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.61803 | 0.190940 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.47214 | 0.687181 | ||||||||
\(191\) | 7.47214 | 0.540665 | 0.270332 | − | 0.962767i | \(-0.412866\pi\) | ||||
0.270332 | + | 0.962767i | \(0.412866\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.5623 | 1.33614 | 0.668072 | − | 0.744097i | \(-0.267120\pi\) | ||||
0.668072 | + | 0.744097i | \(0.267120\pi\) | |||||||
\(194\) | 8.67376 | 0.622740 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.23607 | −0.231148 | ||||||||
\(197\) | 24.3820 | 1.73714 | 0.868572 | − | 0.495564i | \(-0.165039\pi\) | ||||
0.868572 | + | 0.495564i | \(0.165039\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.7082 | −1.18441 | −0.592207 | − | 0.805786i | \(-0.701743\pi\) | ||||
−0.592207 | + | 0.805786i | \(0.701743\pi\) | |||||||
\(200\) | 4.14590 | 0.293159 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.85410 | 0.130454 | ||||||||
\(203\) | −13.4164 | −0.941647 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −31.2705 | −2.18403 | ||||||||
\(206\) | 3.70820 | 0.258363 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.27051 | −0.226769 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.2705 | 1.53317 | 0.766583 | − | 0.642146i | \(-0.221956\pi\) | ||||
0.766583 | + | 0.642146i | \(0.221956\pi\) | |||||||
\(212\) | −15.5623 | −1.06882 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.61803 | 0.178965 | ||||||||
\(215\) | −16.3262 | −1.11344 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.56231 | −0.581247 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.85410 | −0.191988 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.708204 | 0.0474248 | 0.0237124 | − | 0.999719i | \(-0.492451\pi\) | ||||
0.0237124 | + | 0.999719i | \(0.492451\pi\) | |||||||
\(224\) | 16.8541 | 1.12611 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.437694 | 0.0291150 | ||||||||
\(227\) | −24.8885 | −1.65191 | −0.825955 | − | 0.563736i | \(-0.809364\pi\) | ||||
−0.825955 | + | 0.563736i | \(0.809364\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 5.61803 | 0.370442 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.0000 | 0.656532 | ||||||||
\(233\) | 24.3262 | 1.59366 | 0.796832 | − | 0.604200i | \(-0.206507\pi\) | ||||
0.796832 | + | 0.604200i | \(0.206507\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.23607 | −0.276331 | ||||||||
\(236\) | 16.7082 | 1.08761 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.00000 | 0.194461 | ||||||||
\(239\) | 2.56231 | 0.165742 | 0.0828709 | − | 0.996560i | \(-0.473591\pi\) | ||||
0.0828709 | + | 0.996560i | \(0.473591\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.1246 | 1.48959 | 0.744794 | − | 0.667295i | \(-0.232548\pi\) | ||||
0.744794 | + | 0.667295i | \(0.232548\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.7082 | 0.813559 | ||||||||
\(245\) | 5.23607 | 0.334520 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.3262 | 0.657043 | ||||||||
\(248\) | 6.38197 | 0.405255 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.09017 | 0.321931 | ||||||||
\(251\) | 7.79837 | 0.492229 | 0.246114 | − | 0.969241i | \(-0.420846\pi\) | ||||
0.246114 | + | 0.969241i | \(0.420846\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2.29180 | −0.143800 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | 11.6738 | 0.728189 | 0.364095 | − | 0.931362i | \(-0.381378\pi\) | ||||
0.364095 | + | 0.931362i | \(0.381378\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.708204 | −0.0440057 | ||||||||
\(260\) | 7.47214 | 0.463402 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.41641 | 0.272847 | ||||||||
\(263\) | −16.3262 | −1.00672 | −0.503359 | − | 0.864077i | \(-0.667903\pi\) | ||||
−0.503359 | + | 0.864077i | \(0.667903\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.1803 | 1.54682 | ||||||||
\(266\) | −10.8541 | −0.665508 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.4721 | 0.945111 | ||||||||
\(269\) | −15.5279 | −0.946751 | −0.473375 | − | 0.880861i | \(-0.656965\pi\) | ||||
−0.473375 | + | 0.880861i | \(0.656965\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.2705 | 1.65657 | 0.828283 | − | 0.560310i | \(-0.189318\pi\) | ||||
0.828283 | + | 0.560310i | \(0.189318\pi\) | |||||||
\(272\) | 3.00000 | 0.181902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.61803 | 0.278986 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.5623 | −1.83631 | −0.918155 | − | 0.396220i | \(-0.870322\pi\) | ||||
−0.918155 | + | 0.396220i | \(0.870322\pi\) | |||||||
\(278\) | −0.527864 | −0.0316592 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −17.5623 | −1.04955 | ||||||||
\(281\) | −0.763932 | −0.0455724 | −0.0227862 | − | 0.999740i | \(-0.507254\pi\) | ||||
−0.0227862 | + | 0.999740i | \(0.507254\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.180340 | −0.0107201 | −0.00536005 | − | 0.999986i | \(-0.501706\pi\) | ||||
−0.00536005 | + | 0.999986i | \(0.501706\pi\) | |||||||
\(284\) | −9.00000 | −0.534052 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 35.8328 | 2.11514 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.3820 | −0.845998 | ||||||||
\(290\) | −7.23607 | −0.424917 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.23607 | −0.306418 | ||||||||
\(293\) | 0.0557281 | 0.00325567 | 0.00162783 | − | 0.999999i | \(-0.499482\pi\) | ||||
0.00162783 | + | 0.999999i | \(0.499482\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.0344 | −1.57401 | ||||||||
\(296\) | 0.527864 | 0.0306815 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.27051 | −0.537026 | ||||||||
\(299\) | 6.12461 | 0.354195 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.7082 | 1.07832 | ||||||||
\(302\) | 1.23607 | 0.0711277 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.8541 | −0.622525 | ||||||||
\(305\) | −20.5623 | −1.17739 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.562306 | −0.0320925 | −0.0160462 | − | 0.999871i | \(-0.505108\pi\) | ||||
−0.0160462 | + | 0.999871i | \(0.505108\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.61803 | −0.262287 | ||||||||
\(311\) | −2.52786 | −0.143342 | −0.0716710 | − | 0.997428i | \(-0.522833\pi\) | ||||
−0.0716710 | + | 0.997428i | \(0.522833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.8328 | 1.46016 | 0.730079 | − | 0.683363i | \(-0.239483\pi\) | ||||
0.730079 | + | 0.683363i | \(0.239483\pi\) | |||||||
\(314\) | 2.29180 | 0.129334 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.3262 | 0.862168 | ||||||||
\(317\) | 19.3607 | 1.08740 | 0.543702 | − | 0.839278i | \(-0.317022\pi\) | ||||
0.543702 | + | 0.839278i | \(0.317022\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.618034 | −0.0345492 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.43769 | −0.358759 | ||||||||
\(323\) | −9.47214 | −0.527044 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.27051 | −0.181415 | ||||||||
\(326\) | −11.2918 | −0.625395 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −26.7082 | −1.47471 | ||||||||
\(329\) | 4.85410 | 0.267615 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.5967 | 1.46189 | 0.730945 | − | 0.682437i | \(-0.239080\pi\) | ||||
0.730945 | + | 0.682437i | \(0.239080\pi\) | |||||||
\(332\) | −1.14590 | −0.0628893 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.20163 | −0.339338 | ||||||||
\(335\) | −25.0344 | −1.36778 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.291796 | 0.0158951 | 0.00794757 | − | 0.999968i | \(-0.497470\pi\) | ||||
0.00794757 | + | 0.999968i | \(0.497470\pi\) | |||||||
\(338\) | 6.11146 | 0.332419 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.85410 | −0.371716 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | −13.9443 | −0.751825 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.50658 | −0.511077 | ||||||||
\(347\) | −20.9443 | −1.12435 | −0.562174 | − | 0.827019i | \(-0.690035\pi\) | ||||
−0.562174 | + | 0.827019i | \(0.690035\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.1246 | 0.541958 | 0.270979 | − | 0.962585i | \(-0.412653\pi\) | ||||
0.270979 | + | 0.962585i | \(0.412653\pi\) | |||||||
\(350\) | 3.43769 | 0.183752 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.4721 | 0.557376 | 0.278688 | − | 0.960382i | \(-0.410101\pi\) | ||||
0.278688 | + | 0.960382i | \(0.410101\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.5623 | 0.772887 | ||||||||
\(356\) | 0.854102 | 0.0452673 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.38197 | −0.0730392 | ||||||||
\(359\) | −12.7639 | −0.673655 | −0.336827 | − | 0.941566i | \(-0.609354\pi\) | ||||
−0.336827 | + | 0.941566i | \(0.609354\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.2705 | 0.803711 | ||||||||
\(362\) | 10.7984 | 0.567550 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.56231 | −0.448787 | ||||||||
\(365\) | 8.47214 | 0.443452 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.56231 | 0.290350 | 0.145175 | − | 0.989406i | \(-0.453625\pi\) | ||||
0.145175 | + | 0.989406i | \(0.453625\pi\) | |||||||
\(368\) | −6.43769 | −0.335588 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.381966 | −0.0198575 | ||||||||
\(371\) | −28.8541 | −1.49803 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.41641 | 0.228673 | 0.114336 | − | 0.993442i | \(-0.463526\pi\) | ||||
0.114336 | + | 0.993442i | \(0.463526\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.61803 | −0.186586 | ||||||||
\(377\) | −7.88854 | −0.406281 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.58359 | 0.0813437 | 0.0406718 | − | 0.999173i | \(-0.487050\pi\) | ||||
0.0406718 | + | 0.999173i | \(0.487050\pi\) | |||||||
\(380\) | 24.7984 | 1.27213 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.61803 | −0.236279 | ||||||||
\(383\) | −26.8885 | −1.37394 | −0.686970 | − | 0.726686i | \(-0.741060\pi\) | ||||
−0.686970 | + | 0.726686i | \(0.741060\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.4721 | −0.583916 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 22.7082 | 1.15283 | ||||||||
\(389\) | −24.2705 | −1.23056 | −0.615282 | − | 0.788307i | \(-0.710958\pi\) | ||||
−0.615282 | + | 0.788307i | \(0.710958\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.61803 | −0.284116 | ||||||||
\(392\) | 4.47214 | 0.225877 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15.0689 | −0.759159 | ||||||||
\(395\) | −24.7984 | −1.24774 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −38.7082 | −1.94271 | −0.971355 | − | 0.237635i | \(-0.923628\pi\) | ||||
−0.971355 | + | 0.237635i | \(0.923628\pi\) | |||||||
\(398\) | 10.3262 | 0.517608 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.43769 | 0.171885 | ||||||||
\(401\) | 26.0902 | 1.30288 | 0.651440 | − | 0.758700i | \(-0.274165\pi\) | ||||
0.651440 | + | 0.758700i | \(0.274165\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.03444 | −0.250783 | ||||||||
\(404\) | 4.85410 | 0.241501 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.29180 | 0.411515 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.0557 | 0.546671 | 0.273335 | − | 0.961919i | \(-0.411873\pi\) | ||||
0.273335 | + | 0.961919i | \(0.411873\pi\) | |||||||
\(410\) | 19.3262 | 0.954455 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.70820 | 0.478289 | ||||||||
\(413\) | 30.9787 | 1.52436 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.85410 | 0.0910143 | ||||||||
\(416\) | 9.90983 | 0.485869 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.5066 | −0.806399 | −0.403200 | − | 0.915112i | \(-0.632102\pi\) | ||||
−0.403200 | + | 0.915112i | \(0.632102\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.2705 | −1.81645 | −0.908227 | − | 0.418478i | \(-0.862564\pi\) | ||||
−0.908227 | + | 0.418478i | \(0.862564\pi\) | |||||||
\(422\) | −13.7639 | −0.670018 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 21.5066 | 1.04445 | ||||||||
\(425\) | 3.00000 | 0.145521 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.5623 | 1.14026 | ||||||||
\(428\) | 6.85410 | 0.331306 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.0902 | 0.486591 | ||||||||
\(431\) | −39.5066 | −1.90296 | −0.951482 | − | 0.307703i | \(-0.900440\pi\) | ||||
−0.951482 | + | 0.307703i | \(0.900440\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.00000 | −0.288342 | −0.144171 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144171 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(434\) | 5.29180 | 0.254014 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.3262 | 0.972336 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.29180 | −0.157109 | −0.0785544 | − | 0.996910i | \(-0.525030\pi\) | ||||
−0.0785544 | + | 0.996910i | \(0.525030\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.76393 | 0.0839017 | ||||||||
\(443\) | 41.1246 | 1.95389 | 0.976945 | − | 0.213493i | \(-0.0684840\pi\) | ||||
0.976945 | + | 0.213493i | \(0.0684840\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.38197 | −0.0655115 | ||||||||
\(446\) | −0.437694 | −0.0207254 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.708204 | 0.0334595 | ||||||||
\(449\) | 24.4721 | 1.15491 | 0.577456 | − | 0.816422i | \(-0.304046\pi\) | ||||
0.577456 | + | 0.816422i | \(0.304046\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.14590 | 0.0538985 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.3820 | 0.721911 | ||||||||
\(455\) | 13.8541 | 0.649490 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.20163 | −0.383656 | −0.191828 | − | 0.981429i | \(-0.561442\pi\) | ||||
−0.191828 | + | 0.981429i | \(0.561442\pi\) | |||||||
\(458\) | −6.18034 | −0.288788 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14.7082 | 0.685774 | ||||||||
\(461\) | −21.0902 | −0.982267 | −0.491134 | − | 0.871084i | \(-0.663417\pi\) | ||||
−0.491134 | + | 0.871084i | \(0.663417\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.7984 | −0.734213 | −0.367106 | − | 0.930179i | \(-0.619651\pi\) | ||||
−0.367106 | + | 0.930179i | \(0.619651\pi\) | |||||||
\(464\) | 8.29180 | 0.384937 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.0344 | −0.696457 | ||||||||
\(467\) | 9.76393 | 0.451821 | 0.225910 | − | 0.974148i | \(-0.427464\pi\) | ||||
0.225910 | + | 0.974148i | \(0.427464\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.6869 | 1.32464 | ||||||||
\(470\) | 2.61803 | 0.120761 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −23.0902 | −1.06281 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.8541 | −0.498020 | ||||||||
\(476\) | 7.85410 | 0.359992 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.58359 | −0.0724318 | ||||||||
\(479\) | −28.0902 | −1.28347 | −0.641736 | − | 0.766925i | \(-0.721786\pi\) | ||||
−0.641736 | + | 0.766925i | \(0.721786\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.416408 | −0.0189866 | ||||||||
\(482\) | −14.2918 | −0.650973 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −36.7426 | −1.66840 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.8197 | 0.762172 | 0.381086 | − | 0.924540i | \(-0.375550\pi\) | ||||
0.381086 | + | 0.924540i | \(0.375550\pi\) | |||||||
\(488\) | −17.5623 | −0.795008 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.23607 | −0.146191 | ||||||||
\(491\) | 25.2148 | 1.13793 | 0.568964 | − | 0.822363i | \(-0.307345\pi\) | ||||
0.568964 | + | 0.822363i | \(0.307345\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.23607 | 0.325896 | ||||||||
\(494\) | −6.38197 | −0.287138 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.29180 | 0.237609 | ||||||||
\(497\) | −16.6869 | −0.748511 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.5623 | −0.786197 | −0.393098 | − | 0.919496i | \(-0.628597\pi\) | ||||
−0.393098 | + | 0.919496i | \(0.628597\pi\) | |||||||
\(500\) | 13.3262 | 0.595967 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.81966 | −0.215112 | ||||||||
\(503\) | 28.0689 | 1.25153 | 0.625765 | − | 0.780012i | \(-0.284787\pi\) | ||||
0.625765 | + | 0.780012i | \(0.284787\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.85410 | −0.349503 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.00000 | −0.266207 | ||||||||
\(509\) | −23.6180 | −1.04685 | −0.523425 | − | 0.852071i | \(-0.675346\pi\) | ||||
−0.523425 | + | 0.852071i | \(0.675346\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.70820 | −0.429466 | ||||||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.21478 | −0.318230 | ||||||||
\(515\) | −15.7082 | −0.692186 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.437694 | 0.0192312 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.3262 | −0.452835 | ||||||||
\(521\) | 14.8328 | 0.649837 | 0.324919 | − | 0.945742i | \(-0.394663\pi\) | ||||
0.324919 | + | 0.945742i | \(0.394663\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.9787 | 0.523793 | 0.261896 | − | 0.965096i | \(-0.415652\pi\) | ||||
0.261896 | + | 0.965096i | \(0.415652\pi\) | |||||||
\(524\) | 11.5623 | 0.505102 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.0902 | 0.439952 | ||||||||
\(527\) | 4.61803 | 0.201165 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.9443 | −0.475838 | ||||||||
\(530\) | −15.5623 | −0.675983 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −28.4164 | −1.23201 | ||||||||
\(533\) | 21.0689 | 0.912595 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.0902 | −0.479470 | ||||||||
\(536\) | −21.3820 | −0.923560 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.59675 | 0.413745 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.5623 | −0.841049 | −0.420525 | − | 0.907281i | \(-0.638154\pi\) | ||||
−0.420525 | + | 0.907281i | \(0.638154\pi\) | |||||||
\(542\) | −16.8541 | −0.723946 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.09017 | −0.389738 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.6180 | −0.924320 | −0.462160 | − | 0.886796i | \(-0.652925\pi\) | ||||
−0.462160 | + | 0.886796i | \(0.652925\pi\) | |||||||
\(548\) | 12.0902 | 0.516466 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −26.1803 | −1.11532 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.4164 | 1.20839 | ||||||||
\(554\) | 18.8885 | 0.802497 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.38197 | −0.0586084 | ||||||||
\(557\) | 14.9098 | 0.631750 | 0.315875 | − | 0.948801i | \(-0.397702\pi\) | ||||
0.315875 | + | 0.948801i | \(0.397702\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.0000 | 0.465250 | ||||||||
\(560\) | −14.5623 | −0.615370 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.472136 | 0.0199159 | ||||||||
\(563\) | −8.88854 | −0.374607 | −0.187304 | − | 0.982302i | \(-0.559975\pi\) | ||||
−0.187304 | + | 0.982302i | \(0.559975\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.85410 | −0.0780027 | ||||||||
\(566\) | 0.111456 | 0.00468485 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.4377 | 0.521874 | ||||||||
\(569\) | −24.0689 | −1.00902 | −0.504510 | − | 0.863406i | \(-0.668327\pi\) | ||||
−0.504510 | + | 0.863406i | \(0.668327\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.6869 | −1.45160 | −0.725801 | − | 0.687905i | \(-0.758531\pi\) | ||||
−0.725801 | + | 0.687905i | \(0.758531\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −22.1459 | −0.924352 | ||||||||
\(575\) | −6.43769 | −0.268470 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.7639 | 0.448108 | 0.224054 | − | 0.974577i | \(-0.428071\pi\) | ||||
0.224054 | + | 0.974577i | \(0.428071\pi\) | |||||||
\(578\) | 8.88854 | 0.369715 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −18.9443 | −0.786618 | ||||||||
\(581\) | −2.12461 | −0.0881437 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 7.23607 | 0.299431 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.0344419 | −0.00142278 | ||||||||
\(587\) | 38.3050 | 1.58101 | 0.790507 | − | 0.612453i | \(-0.209817\pi\) | ||||
0.790507 | + | 0.612453i | \(0.209817\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.7082 | −0.688450 | ||||||||
\(590\) | 16.7082 | 0.687866 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.437694 | 0.0179891 | ||||||||
\(593\) | 22.2148 | 0.912252 | 0.456126 | − | 0.889915i | \(-0.349237\pi\) | ||||
0.456126 | + | 0.889915i | \(0.349237\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.7082 | −0.520986 | ||||||||
\(596\) | −24.2705 | −0.994159 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.78522 | −0.154789 | ||||||||
\(599\) | 8.29180 | 0.338794 | 0.169397 | − | 0.985548i | \(-0.445818\pi\) | ||||
0.169397 | + | 0.985548i | \(0.445818\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.8328 | −1.38007 | −0.690035 | − | 0.723776i | \(-0.742405\pi\) | ||||
−0.690035 | + | 0.723776i | \(0.742405\pi\) | |||||||
\(602\) | −11.5623 | −0.471244 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.23607 | 0.131674 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.3262 | −0.540895 | −0.270448 | − | 0.962735i | \(-0.587172\pi\) | ||||
−0.270448 | + | 0.962735i | \(0.587172\pi\) | |||||||
\(608\) | 32.8885 | 1.33381 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.7082 | 0.514540 | ||||||||
\(611\) | 2.85410 | 0.115465 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.6525 | −1.39960 | −0.699800 | − | 0.714339i | \(-0.746728\pi\) | ||||
−0.699800 | + | 0.714339i | \(0.746728\pi\) | |||||||
\(614\) | 0.347524 | 0.0140249 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.5836 | −0.788406 | −0.394203 | − | 0.919023i | \(-0.628979\pi\) | ||||
−0.394203 | + | 0.919023i | \(0.628979\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.81966 | −0.354492 | −0.177246 | − | 0.984167i | \(-0.556719\pi\) | ||||
−0.177246 | + | 0.984167i | \(0.556719\pi\) | |||||||
\(620\) | −12.0902 | −0.485553 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.56231 | 0.0626428 | ||||||||
\(623\) | 1.58359 | 0.0634453 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.8328 | −1.23331 | ||||||||
\(626\) | −15.9656 | −0.638112 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.00000 | 0.239426 | ||||||||
\(629\) | 0.381966 | 0.0152300 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.2705 | 1.84200 | 0.921000 | − | 0.389563i | \(-0.127374\pi\) | ||||
0.921000 | + | 0.389563i | \(0.127374\pi\) | |||||||
\(632\) | −21.1803 | −0.842509 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.9656 | −0.475213 | ||||||||
\(635\) | 9.70820 | 0.385258 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.52786 | −0.139779 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 29.7984 | 1.17788 | ||||||||
\(641\) | −35.7426 | −1.41175 | −0.705875 | − | 0.708337i | \(-0.749446\pi\) | ||||
−0.705875 | + | 0.708337i | \(0.749446\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.5623 | −1.52075 | −0.760374 | − | 0.649485i | \(-0.774985\pi\) | ||||
−0.760374 | + | 0.649485i | \(0.774985\pi\) | |||||||
\(644\) | −16.8541 | −0.664145 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.85410 | 0.230327 | ||||||||
\(647\) | −27.7984 | −1.09287 | −0.546433 | − | 0.837503i | \(-0.684015\pi\) | ||||
−0.546433 | + | 0.837503i | \(0.684015\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.02129 | 0.0792814 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −29.5623 | −1.15775 | ||||||||
\(653\) | −51.0344 | −1.99713 | −0.998566 | − | 0.0535342i | \(-0.982951\pi\) | ||||
−0.998566 | + | 0.0535342i | \(0.982951\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.7082 | −0.730990 | ||||||||
\(656\) | −22.1459 | −0.864652 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.00000 | −0.116952 | ||||||||
\(659\) | −10.6525 | −0.414962 | −0.207481 | − | 0.978239i | \(-0.566526\pi\) | ||||
−0.207481 | + | 0.978239i | \(0.566526\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.90983 | −0.385448 | −0.192724 | − | 0.981253i | \(-0.561732\pi\) | ||||
−0.192724 | + | 0.981253i | \(0.561732\pi\) | |||||||
\(662\) | −16.4377 | −0.638869 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.58359 | 0.0614553 | ||||||||
\(665\) | 45.9787 | 1.78298 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.5279 | −0.601241 | ||||||||
\(668\) | −16.2361 | −0.628192 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 15.4721 | 0.597741 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.4164 | −0.478617 | −0.239309 | − | 0.970944i | \(-0.576921\pi\) | ||||
−0.239309 | + | 0.970944i | \(0.576921\pi\) | |||||||
\(674\) | −0.180340 | −0.00694643 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.0000 | 0.615385 | ||||||||
\(677\) | 13.5279 | 0.519918 | 0.259959 | − | 0.965620i | \(-0.416291\pi\) | ||||
0.259959 | + | 0.965620i | \(0.416291\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 42.1033 | 1.61578 | ||||||||
\(680\) | 9.47214 | 0.363240 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.11146 | 0.119057 | 0.0595283 | − | 0.998227i | \(-0.481040\pi\) | ||||
0.0595283 | + | 0.998227i | \(0.481040\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.5623 | −0.747437 | ||||||||
\(686\) | −9.27051 | −0.353950 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −11.5623 | −0.440809 | ||||||||
\(689\) | −16.9656 | −0.646336 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.2918 | −1.00019 | −0.500094 | − | 0.865971i | \(-0.666701\pi\) | ||||
−0.500094 | + | 0.865971i | \(0.666701\pi\) | |||||||
\(692\) | −24.8885 | −0.946120 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.9443 | 0.491358 | ||||||||
\(695\) | 2.23607 | 0.0848189 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.3262 | −0.732033 | ||||||||
\(698\) | −6.25735 | −0.236844 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.00000 | 0.340168 | ||||||||
\(701\) | −10.6869 | −0.403639 | −0.201820 | − | 0.979423i | \(-0.564685\pi\) | ||||
−0.201820 | + | 0.979423i | \(0.564685\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.38197 | −0.0521218 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.47214 | −0.243582 | ||||||||
\(707\) | 9.00000 | 0.338480 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 48.7426 | 1.83057 | 0.915284 | − | 0.402809i | \(-0.131966\pi\) | ||||
0.915284 | + | 0.402809i | \(0.131966\pi\) | |||||||
\(710\) | −9.00000 | −0.337764 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.18034 | −0.0442351 | ||||||||
\(713\) | −9.90983 | −0.371126 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.61803 | −0.135212 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.88854 | 0.294398 | ||||||||
\(719\) | 1.58359 | 0.0590580 | 0.0295290 | − | 0.999564i | \(-0.490599\pi\) | ||||
0.0295290 | + | 0.999564i | \(0.490599\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.0000 | 0.670355 | ||||||||
\(722\) | −9.43769 | −0.351235 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 28.2705 | 1.05067 | ||||||||
\(725\) | 8.29180 | 0.307950 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.8541 | 1.44102 | 0.720509 | − | 0.693445i | \(-0.243908\pi\) | ||||
0.720509 | + | 0.693445i | \(0.243908\pi\) | |||||||
\(728\) | 11.8328 | 0.438553 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.23607 | −0.193796 | ||||||||
\(731\) | −10.0902 | −0.373198 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.7082 | 1.39278 | 0.696392 | − | 0.717661i | \(-0.254787\pi\) | ||||
0.696392 | + | 0.717661i | \(0.254787\pi\) | |||||||
\(734\) | −3.43769 | −0.126888 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19.5066 | 0.719022 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.0000 | 0.919640 | 0.459820 | − | 0.888012i | \(-0.347914\pi\) | ||||
0.459820 | + | 0.888012i | \(0.347914\pi\) | |||||||
\(740\) | −1.00000 | −0.0367607 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17.8328 | 0.654663 | ||||||||
\(743\) | 35.1803 | 1.29064 | 0.645321 | − | 0.763912i | \(-0.276724\pi\) | ||||
0.645321 | + | 0.763912i | \(0.276724\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 39.2705 | 1.43876 | ||||||||
\(746\) | −2.72949 | −0.0999337 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.7082 | 0.464348 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.9230 | 0.435076 | 0.217538 | − | 0.976052i | \(-0.430197\pi\) | ||||
0.217538 | + | 0.976052i | \(0.430197\pi\) | |||||||
\(752\) | −3.00000 | −0.109399 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.87539 | 0.177551 | ||||||||
\(755\) | −5.23607 | −0.190560 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.94427 | 0.0706658 | 0.0353329 | − | 0.999376i | \(-0.488751\pi\) | ||||
0.0353329 | + | 0.999376i | \(0.488751\pi\) | |||||||
\(758\) | −0.978714 | −0.0355485 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −34.2705 | −1.24312 | ||||||||
\(761\) | −30.8885 | −1.11971 | −0.559854 | − | 0.828591i | \(-0.689143\pi\) | ||||
−0.559854 | + | 0.828591i | \(0.689143\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12.0902 | −0.437407 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.6180 | 0.600434 | ||||||||
\(767\) | 18.2148 | 0.657698 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.6869 | −0.457502 | −0.228751 | − | 0.973485i | \(-0.573464\pi\) | ||||
−0.228751 | + | 0.973485i | \(0.573464\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −30.0344 | −1.08096 | ||||||||
\(773\) | 31.2492 | 1.12396 | 0.561978 | − | 0.827152i | \(-0.310040\pi\) | ||||
0.561978 | + | 0.827152i | \(0.310040\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.29180 | 0.190087 | ||||||||
\(776\) | −31.3820 | −1.12655 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.0000 | 0.537776 | ||||||||
\(779\) | 69.9230 | 2.50525 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 3.47214 | 0.124163 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.70820 | 0.132436 | ||||||||
\(785\) | −9.70820 | −0.346501 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.2918 | 0.366863 | 0.183431 | − | 0.983033i | \(-0.441279\pi\) | ||||
0.183431 | + | 0.983033i | \(0.441279\pi\) | |||||||
\(788\) | −39.4508 | −1.40538 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 15.3262 | 0.545283 | ||||||||
\(791\) | 2.12461 | 0.0755425 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.8541 | 0.491974 | ||||||||
\(794\) | 23.9230 | 0.848995 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 27.0344 | 0.958210 | ||||||||
\(797\) | −10.7639 | −0.381278 | −0.190639 | − | 0.981660i | \(-0.561056\pi\) | ||||
−0.190639 | + | 0.981660i | \(0.561056\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.61803 | −0.0926194 | ||||||||
\(800\) | −10.4164 | −0.368276 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16.1246 | −0.569380 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 27.2705 | 0.961159 | ||||||||
\(806\) | 3.11146 | 0.109596 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.70820 | −0.235994 | ||||||||
\(809\) | 9.67376 | 0.340111 | 0.170056 | − | 0.985434i | \(-0.445605\pi\) | ||||
0.170056 | + | 0.985434i | \(0.445605\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.25735 | −0.114381 | −0.0571906 | − | 0.998363i | \(-0.518214\pi\) | ||||
−0.0571906 | + | 0.998363i | \(0.518214\pi\) | |||||||
\(812\) | 21.7082 | 0.761809 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 47.8328 | 1.67551 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.5066 | 1.27720 | ||||||||
\(818\) | −6.83282 | −0.238904 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 50.5967 | 1.76692 | ||||||||
\(821\) | 40.4164 | 1.41054 | 0.705271 | − | 0.708938i | \(-0.250825\pi\) | ||||
0.705271 | + | 0.708938i | \(0.250825\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.4721 | −1.23648 | −0.618240 | − | 0.785989i | \(-0.712154\pi\) | ||||
−0.618240 | + | 0.785989i | \(0.712154\pi\) | |||||||
\(824\) | −13.4164 | −0.467383 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −19.1459 | −0.666171 | ||||||||
\(827\) | 53.1246 | 1.84732 | 0.923662 | − | 0.383208i | \(-0.125181\pi\) | ||||
0.923662 | + | 0.383208i | \(0.125181\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.6869 | 0.614292 | 0.307146 | − | 0.951662i | \(-0.400626\pi\) | ||||
0.307146 | + | 0.951662i | \(0.400626\pi\) | |||||||
\(830\) | −1.14590 | −0.0397747 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.416408 | 0.0144363 | ||||||||
\(833\) | 3.23607 | 0.112123 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.2705 | 0.909128 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.2016 | 0.352409 | ||||||||
\(839\) | 36.7082 | 1.26731 | 0.633654 | − | 0.773617i | \(-0.281554\pi\) | ||||
0.633654 | + | 0.773617i | \(0.281554\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 23.0344 | 0.793819 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −36.0344 | −1.24036 | ||||||||
\(845\) | −25.8885 | −0.890593 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 17.8328 | 0.612381 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.85410 | −0.0635952 | ||||||||
\(851\) | −0.819660 | −0.0280976 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.94427 | 0.340485 | 0.170243 | − | 0.985402i | \(-0.445545\pi\) | ||||
0.170243 | + | 0.985402i | \(0.445545\pi\) | |||||||
\(854\) | −14.5623 | −0.498312 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.47214 | −0.323751 | ||||||||
\(857\) | 47.7214 | 1.63013 | 0.815065 | − | 0.579369i | \(-0.196701\pi\) | ||||
0.815065 | + | 0.579369i | \(0.196701\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.11146 | 0.242640 | 0.121320 | − | 0.992613i | \(-0.461287\pi\) | ||||
0.121320 | + | 0.992613i | \(0.461287\pi\) | |||||||
\(860\) | 26.4164 | 0.900792 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.4164 | 0.831626 | ||||||||
\(863\) | −11.8885 | −0.404691 | −0.202345 | − | 0.979314i | \(-0.564856\pi\) | ||||
−0.202345 | + | 0.979314i | \(0.564856\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.2705 | 1.36924 | ||||||||
\(866\) | 3.70820 | 0.126010 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13.8541 | 0.470239 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.8673 | 0.571525 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12.5623 | −0.424926 | ||||||||
\(875\) | 24.7082 | 0.835290 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.41641 | −0.216667 | −0.108333 | − | 0.994115i | \(-0.534551\pi\) | ||||
−0.108333 | + | 0.994115i | \(0.534551\pi\) | |||||||
\(878\) | 2.03444 | 0.0686591 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.9098 | −0.468634 | −0.234317 | − | 0.972160i | \(-0.575285\pi\) | ||||
−0.234317 | + | 0.972160i | \(0.575285\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.5836 | 0.356166 | 0.178083 | − | 0.984015i | \(-0.443010\pi\) | ||||
0.178083 | + | 0.984015i | \(0.443010\pi\) | |||||||
\(884\) | 4.61803 | 0.155321 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25.4164 | −0.853881 | ||||||||
\(887\) | 3.00000 | 0.100730 | 0.0503651 | − | 0.998731i | \(-0.483962\pi\) | ||||
0.0503651 | + | 0.998731i | \(0.483962\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.1246 | −0.373108 | ||||||||
\(890\) | 0.854102 | 0.0286296 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.14590 | −0.0383675 | ||||||||
\(893\) | 9.47214 | 0.316973 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.85410 | 0.195681 | ||||||||
\(896\) | −34.1459 | −1.14073 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.1246 | −0.504715 | ||||||||
\(899\) | 12.7639 | 0.425701 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.5623 | 0.518456 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.58359 | −0.0526695 | ||||||||
\(905\) | −45.7426 | −1.52054 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.9787 | −1.42708 | −0.713542 | − | 0.700612i | \(-0.752910\pi\) | ||||
−0.713542 | + | 0.700612i | \(0.752910\pi\) | |||||||
\(908\) | 40.2705 | 1.33642 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.56231 | −0.283838 | ||||||||
\(911\) | −18.0557 | −0.598213 | −0.299106 | − | 0.954220i | \(-0.596689\pi\) | ||||
−0.299106 | + | 0.954220i | \(0.596689\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 5.06888 | 0.167664 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.1803 | −0.534613 | ||||||||
\(917\) | 21.4377 | 0.707935 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46.9574 | −1.54898 | −0.774491 | − | 0.632585i | \(-0.781994\pi\) | ||||
−0.774491 | + | 0.632585i | \(0.781994\pi\) | |||||||
\(920\) | −20.3262 | −0.670136 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.0344 | 0.429266 | ||||||||
\(923\) | −9.81153 | −0.322950 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.437694 | 0.0143913 | ||||||||
\(926\) | 9.76393 | 0.320863 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −25.1246 | −0.824756 | ||||||||
\(929\) | 32.8885 | 1.07904 | 0.539519 | − | 0.841973i | \(-0.318606\pi\) | ||||
0.539519 | + | 0.841973i | \(0.318606\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.7082 | −0.383721 | ||||||||
\(932\) | −39.3607 | −1.28930 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.03444 | −0.197453 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.5967 | 0.542192 | 0.271096 | − | 0.962552i | \(-0.412614\pi\) | ||||
0.271096 | + | 0.962552i | \(0.412614\pi\) | |||||||
\(938\) | −17.7295 | −0.578888 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.85410 | 0.223556 | ||||||||
\(941\) | −44.6312 | −1.45494 | −0.727468 | − | 0.686142i | \(-0.759303\pi\) | ||||
−0.727468 | + | 0.686142i | \(0.759303\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41.4721 | 1.35052 | ||||||||
\(944\) | −19.1459 | −0.623146 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.3262 | −0.595523 | −0.297761 | − | 0.954640i | \(-0.596240\pi\) | ||||
−0.297761 | + | 0.954640i | \(0.596240\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.70820 | −0.185296 | ||||||||
\(950\) | 6.70820 | 0.217643 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.8541 | −0.351783 | ||||||||
\(953\) | 37.8197 | 1.22510 | 0.612549 | − | 0.790432i | \(-0.290144\pi\) | ||||
0.612549 | + | 0.790432i | \(0.290144\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.5623 | 0.633021 | ||||||||
\(956\) | −4.14590 | −0.134088 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.3607 | 0.560898 | ||||||||
\(959\) | 22.4164 | 0.723864 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.8541 | −0.737229 | ||||||||
\(962\) | 0.257354 | 0.00829743 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −37.4164 | −1.20510 | ||||||||
\(965\) | 48.5967 | 1.56438 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.6869 | 1.11546 | 0.557728 | − | 0.830024i | \(-0.311673\pi\) | ||||
0.557728 | + | 0.830024i | \(0.311673\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 22.7082 | 0.729116 | ||||||||
\(971\) | −37.7771 | −1.21232 | −0.606162 | − | 0.795341i | \(-0.707292\pi\) | ||||
−0.606162 | + | 0.795341i | \(0.707292\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.56231 | −0.0821438 | ||||||||
\(974\) | −10.3951 | −0.333081 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.5623 | −0.466128 | ||||||||
\(977\) | 4.63932 | 0.148425 | 0.0742125 | − | 0.997242i | \(-0.476356\pi\) | ||||
0.0742125 | + | 0.997242i | \(0.476356\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −8.47214 | −0.270632 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.5836 | −0.497292 | ||||||||
\(983\) | 27.3050 | 0.870893 | 0.435446 | − | 0.900215i | \(-0.356591\pi\) | ||||
0.435446 | + | 0.900215i | \(0.356591\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 63.8328 | 2.03388 | ||||||||
\(986\) | −4.47214 | −0.142422 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16.7082 | −0.531559 | ||||||||
\(989\) | 21.6525 | 0.688509 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.2705 | 0.675680 | 0.337840 | − | 0.941204i | \(-0.390304\pi\) | ||||
0.337840 | + | 0.941204i | \(0.390304\pi\) | |||||||
\(992\) | −16.0344 | −0.509094 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.3131 | 0.327111 | ||||||||
\(995\) | −43.7426 | −1.38674 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.9787 | 0.411040 | 0.205520 | − | 0.978653i | \(-0.434111\pi\) | ||||
0.205520 | + | 0.978653i | \(0.434111\pi\) | |||||||
\(998\) | 10.8541 | 0.343581 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))